Generalizations of the riesz convergence theorem for lorentz spaces

Abstract

We generalize the classical Riesz convergence theorem to Lorentz spaces, i.e., if f, f1, f2,... ε Lp,q such that fn → f (a.e. or in measure) and ∥fn∥ p,q → ∥f∥p,q, then ∥fn - f∥p,q → 0 as n → ∞. © 2005 Akadémiai Kiadó, Budapest.